Hydroelastic Response of VLFS with An Attached Submerged Horizontal Solid/Porous Plate Under Wave Action

The hydroelastic responses of a submerged horizontal solid/porous plate attached at the front of a very large rectangular floating structure(VLFS)under wave action has been investigated in the context of linear water wave theory.Darcy’s law is adopted to represent energy dissipation in pores.It is assumed that the porous plates are made of material with very fine pores so that the normal velocity across the perforated porous is linearly associated with the pressure drop.In the analytic method,the eigenfunction expansion-matching method(EEMM)for multiple domains is applied to solve the hydrodynamic problem and the elastic equation of motion is solved by the modal expansion method.The performance of the proposed submerged horizontal solid/porous plate can be significantly enhanced by selecting optimal design parameters,such as plate length,horizontal position,submerged depth and porosity.It is concluded that good damping effect can be achieved through installation of solid and porous plate.Porous plate has better damping effect at low frequencies,while solid plate has better damping effect at high frequencies.The optimal ratio of plate length to water depth is 0.25-0.375,and the optimal ratio of submerged depth to water depth is 0.09-0.181.

A SPECIAL SOLUTION OF WAVE DISSIPATION BY FINITE POROUS PLATES

The reflection and transmission of water waves caused by a small amplitude incident wave through finite fine porous plates with equal spacing and permeability in an infinitely long open channel of constant water depth and zero slope are studied. A special solution is obtained when the distance between the two neighbouring plates is an integral multiple of the half-wavelength of the incident wave. It is found that when the dimensionless porous-effect parameter G0 is equal to half the total plate number, the wave dissipation reaches a maximum, and only 50% of the incident wave energy remains in the reflected and transmitted waves. Meanwhile, the reflected and transmitted waves have the same amplitude.

Visco-elastic fluid flow past an infinite vertical porous plate in the presence of first-order chemical reaction

An analysis has been developed to study the unsteady free convection flow of an incompressible visco-elastic fluid on a continuously moving vertical porous plate in the presence of a first-order chemical reaction. The governing equations are solved numerically using an implicit finite difference technique. The obtained numerical solutions are compared with the analytical solutions. The velocity profiles are presented. A parametric analysis is performed to illustrate the influences of the visco-elastic parameter, the dimensionless chemical reaction parameter, and the plate moving velocity on the steady state velocity profiles, the time dependent friction coefficient, the Nusselt number, and the Sherwood number.

Natural vibration of cantilever porous twisted plate with variable thickness in different directions

In this paper,the blade is assumed to be a rotating variable thickness cantilever twisted plate structure,and the natural vibrations of variable thickness cantilever twisted plate made of metal porous material are studied.It is assumed that the thickness of the plate changes along spanwise direction and chordwise direction,respectively,and it changes in both directions.The classical thin shell theory,the first and second fundamental forms of surface and von Karman geometric relationship are employed to derive the total potential energy and kinetic energy of the cantilever twisted plate,in which the centrifugal force potential due to high rotational speed is included.Then,according to the Rayleigh-Ritz procedure and applying the polynomial functions which satisfy the cantilever boundary conditions,the dynamic system expressed by equations of motion is reduced to an eigenvalue problem.By numerical simulation,the frequency curves and the mode shapes of the twisted plate can be obtained to reveal the internal connection between natural vibration and the parameters.A series of comparison studies are performed to verify the accuracy of the present formulation and calculations,in which compared data come from experimental,finite element method and theoretical calculation,respectively.The influence of pre-twist angle,three different forms of thickness taper ratio and rotational speed on natural vibration,mode exchange and frequency veering phenomenon of the system is discussed in detail.In addition,the approach proposed here can efficiently extract analytical expressions of mode functions for rotating variable thickness cantilever twisted plate structures.

Analyses of dynamic characteristics of a fluid-filled thin rectangular porous plate with various boundary conditions

Based on the classical theory of thin plate and Biot theory, a precise model of the transverse vibrations of a thin rectangular porous plate is proposed. The first order differential equations of the porous plate are derived in the frequency domain. By considering the coupling effect between the solid phase and the fluid phase and without any hypothesis for the fluid displacement, the model presented here is rigorous and close to the real materials. Owing to the use of extended homogeneous capacity precision integration method and precise element method, the model can be applied in higher frequency range than pure numerical methods. This model also easily adapts to various boundary conditions. Numerical results are given for two different porous plates under different excitations and boundary conditions.

Analytical Solution for Time-dependent Flow of a Third Grade Fluid Induced Due to Impulsive Motion of a Flat Porous Plate

The aim of the present communication is to discuss the analytical solution for the unsteady flow of a third grade fluid which occupies the space y 〉 0 over an infinite porous plate. The flow is generated due to the motion of the plate in its own plane with an impulsive velocity V（t）. Translational symmetries in variables t and y are utilized to reduce the governing non-linear partial differential equation into an ordinary differential equation. The reduced problem is then solved using homotopy analysis method（HAM）. Graphs representing the solution are plotted and discussed and proper conclusions are drawn.

Radiative Effect on Flow and Heat Transfer over a Vertically Oscillating Porous Flat Plate Embedded in Porous Medium with Oscillating Surface Temperature

The effect of radiation on flow and heat transfer over a vertically oscillating porous flat plate embedded in porous medium with oscillating surface temperature is investigated. The analytic solutions of momentum and energy equations are obtained. The velocity and temperature profiles are computed. The frictional force at the plate due to viscosity of fluid is estimated in terms of non dimensional skin friction coefficient and heat convection at the plate is estimated in the form of Nusselt number. The effects of physical parameters Prandtl number Pr, Grashof number Gr, Suction parameter S and radiative parameter R on velocity and temperature profiles are analyzed through graphs. The effects of oscillation on the velocity and temperature profiles are shown through 3-D surface plot.

Influence of porosity distribution on nonlinear free vibration and transient responses of porous functionally graded skew plates

This article deals with the investigation of the effects of porosity distributions on nonlinear free vibration and transient analysis of porous functionally graded skew(PFGS)plates.The effective material properties of the PFGS plates are obtained from the modified power-law equations in which gradation varies through the thickness of the PFGS plate.A nonlinear finite element(FE)formulation for the overall PFGS plate is derived by adopting first-order shear deformation theory(FSDT)in conjunction with von Karman’s nonlinear strain displacement relations.The governing equations of the PFGS plate are derived using the principle of virtual work.The direct iterative method and Newmark’s integration technique are espoused to solve nonlinear mathematical relations.The influences of the porosity distributions and porosity parameter indices on the nonlinear frequency responses of the PFGS plate for different skew angles are studied in various parameters.The effects of volume fraction grading index and skew angle on the plate’s nonlinear dynamic responses for various porosity distributions are illustrated in detail.

Experimental Study on Wave Attenuation Performance of A New Type of Floating Breakwater with Twin Pontoons and Multi Porous Vertical Plates

A floating breakwater(FB)has extensive potential applications in the fields of coastal,offshore,and ocean engineering owing to its advantages such as eco-friendliness,low cost,easy and rapid construction,and quick dismantling and reinstallation.An FB composed of twin pontoons and multi-porous vertical plates is proposed to improve the wave attenuation performance.The wave attenuation performance is investigated for different FB structures and vertical plate types under different incident wave heights and periods using 2D wave physical model tests in a wave flume.The results demonstrate that the proposed FB has a better performance than that of the conventional single pontoon-type FB.It reduces the wave transmission due to its enhanced wave reflection and energy loss.The wave transmission coefficient of the proposed FB decreases with an increase in the number of layers and relative draft depth of the vertical plates.However,a further decrease in the wave transmission coefficient is not observed when the number of porous vertical plates is increased from 4 to 5 layers.An equation has been derived to predict the wave transmission of the proposed FB based on the experimental results.

Static and free vibration analyses of functionally graded porous variable-thickness plates using an edge-based smoothed finite element method

The main purpose of this paper is to present numerical results of static bending and free vibration of functionally graded porous(FGP) variable-thickness plates by using an edge-based smoothed finite element method(ES-FEM) associate with the mixed interpolation of tensorial components technique for the three-node triangular element(MITC3), so-called ES-MITC3. This ES-MITC3 element is performed to eliminate the shear locking problem and to enhance the accuracy of the existing MITC3 element. In the ES-MITC3 element, the stiffness matrices are obtained by using the strain smoothing technique over the smoothing domains formed by two adjacent MITC3 triangular elements sharing an edge. Materials of the plate are FGP with a power-law index(k) and maximum porosity distributions(U) in the forms of cosine functions. The influences of some geometric parameters, material properties on static bending, and natural frequency of the FGP variable-thickness plates are examined in detail.

Vibration and sound transmission loss characteristics of porous foam functionally graded sandwich panels in thermal environment

This study investigates the vibration and acoustic properties of porous foam functionally graded(FG)plates under the influence of the temperature field.The dynamics equations of the system are established based on Hamilton's principle by using the higher-order shear deformation theory under the linear displacement-strain assumption.The displacement shape function is assumed according to the four-sided simply-supported(SSSS)boundary condition,and the characteristic equations of the system are derived by combining the motion control equations.The theoretical model of vibro-acoustic coupling is established by using the acoustic theory and fluid-structure coupling solution method under the simple harmonic acoustic wave.The system's natural frequency and sound transmission loss(STL)are obtained through programming calculations and compared with the literature and COMSOL simulation to verify the validity and reliability of the theoretical model.The effects of various factors,such as temperature,porosity coefficients,gradient index,core thickness,width-to-thickness ratio on the vibration,and STL characteristics of the system,are discussed.The results provide a theoretical basis for the application of porous foam FG plates in engineering to optimize vibration and sound transmission properties.

Finite element analysis of functionally graded sandwich plates with porosity via a new hyperbolic shear deformation theory

This study focusses on establishing the finite element model based on a new hyperbolic sheareformation theory to investigate the static bending,free vibration,and buckling of the functionally graded sandwich plates with porosity.The novel sandwich plate consists of one homogenous ceramic core and two different functionally graded face sheets which can be widely applied in many fields of engineering and defence technology.The discrete governing equations of motion are carried out via Hamilton’s principle and finite element method.The computation program is coded in MATLAB software and used to study the mechanical behavior of the functionally graded sandwich plate with porosity.The present finite element algorithm can be employed to study the plates with arbitrary shape and boundary conditions.The obtained results are compared with available results in the literature to confirm the reliability of the present algorithm.Also,a comprehensive investigation of the effects of several parameters on the bending,free vibration,and buckling response of functionally graded sandwich plates is presented.The numerical results shows that the distribution of porosity plays significant role on the mechanical behavior of the functionally graded sandwich plates。

由耦合多孔结构和浸没式多孔板引起的波浪能阻尼

The present study investigates the wave-damping characteristics due to the combination of bottom-standing porous structure,submerged porous plate,and fully-extended porous structure of finite width using the small amplitude wave theory.The hydrodynamic characteristics such as reflection,transmission,and dissipation coefficients are determined to analyse the wave energy dissipation by the composite breakwater using the matched eigenfunction expansion method and orthogonal mode-coupling relation.Darcy’s law is incorporated to the flow through porous media.The composite breakwater system is investigated experimentally to validate and compare the numerical results with the physical model study.The complex porous effect parameter for the submerged plate is incorporated in the numerical analysis,which represents the reactance and resistance of the porous structure.The wave forces on the submerged plate and porous structure for the composite breakwater are investigated by considering the effects of changing parameters such as structural porosity,plate submergence,angle of incidence,width of the submerged porous structure and distance between the structures.The study illustrates that the increasing width of the fully-extended porous structure improves the performance of the breakwater system.The proposed study on the composite breakwater yields an useful information for wave energy attenuation,which can be designed and implemented in coastal and harbour areas to achieve wave tranquillity.

The Reflection of Normal Incident Waves by Absorbing-Type Breakwaters

This paper investigates the reflection of normal incident waves produced by absorbing-type breakwaters. The absorbing-type breakwaters in this study consist of a vertical porous plate, a submerged permeable caisson, and an impermeable back wall. The flow field is divided into four regions： a porous caisson region, and three pure water regions. Under the assumptions of linear wave theory, Darcy＇s law in the perforated wall, and the pore velocity potential theory of Sollitt and Cross （1972） in the porons caisson region, this study creates a 2-D BEM model to calculate the reflection coefficients of water waves using several breakwater properties. This numerical model is calibrated by previous numerical studies and limiting cases for a partially perforated-wall caisson breakwater and a vertical porous breakwater with an impermeable back wall. Generally speaking, the wave dissipation in absorbing-type breakwaters is bigger than that for a partially perforatedwall caisson breakwater. The reflection coefficient values imply the performance of wave absorbers in this study. Therefore, we examine the major factors that affect the reflection coefficient.

Experimental study of a 3D printed permanent implantable porous Ta-coated bone plate for fracture fixation

Metal plates have always been the gold standard in the clinic for internal fracture fixation due to their high strength advantages.However,high elastic modulus can cause stress shielding and lead to bone embrittlement.This study used an electron beam melting method to prepare personalized porous Ti6Al4V(pTi)bone plates.Then,chemical vapor deposition(CVD)technology coats tantalum(Ta)metal on the pTi bone plates.The prepared porous Ta-coated bone plate has an elastic modulus similar to cortical bone,and no stress shielding occurred.In vitro experiments showed that compared with pTi plates,Ta coating significantly enhances the attachment and proliferation of cells on the surface of the scaffold.To better evaluate the function of the Ta-coated bone plate,animal experiments were conducted using a coat tibia fracture model.Our results showed that the Ta-coated bone plate could effectively fix the fracture.Both imaging and histological analysis showed that the Ta-coated bone plate had prominent indirect binding of callus formation.Histological results showed that new bone grew at the interface and formed good osseointegration with the host bone.Therefore,this study provides an alternative to bio-functional Ta-coated bone plates with improved osseointegration and osteogenic functions for orthopaedic applications.

A Numerical Tackling on Sakiadis Flow with Thermal Radiation

Momentum and energy laminar boundary layers of an incompressible fluid with thermal radiation about a moving plate in a quiescent ambient fluid are investigated numerically. Also, it has been underlined that the analysis of the roles of both velocity and temperature gradient at infinity is of key relevance for our results.

THE EFFECT OF LONGITUDINAL OSCILLATIONS ON FREE CONVECTION FROM A VERTICAL PLATE EMBEDDED IN A POROUS MEDIUM

In this paper oscillatory 2-D natural convection from a vertical isothermal wall embedded in a po- rous medium, and originating from the oscillation of longitudinal fluid flow, has been investigated both analytically and numerically. Two asymptotic solutions, valid for large and small values of dimensionless frequency γ respectively, are obtained in the closed form. In the range where the asymptotic solutions break down, numerical results to the governing equations are obtained by local similarity meth- od. Both numerical and analytical results show that pulsatory components of the flow and heat transfer depend only on the parameter γ, and the effect of longitudinal oscillation is to decrease the magnitude or' pulsatory Nusselt number with a phase lag between 0 and 90 deg. A correlation for pulsatory heat trans- fer rates is proposed in the whole range of γ within 3% accuracy compared with the numerical results.

Unsteady time-dependent incompressible Newtonian fluid flow between two parallel plates by homotopy analysis method(HAM),homotopy perturbation method(HPM)and collocation method(CM)

Analytical and numerical analyses have performed to study the problem of the flow of incompressible Newtonian fluid between two parallel plates approaching or receding from each other symmetrically.The Navier–Stokes equations have been transformed into an ordinary differential equation using a similarity transformation.The powerful analytical methods called collocation method(CM),the homotopy perturbation method(HPM),and the homotopy analysis method(HAM)have been used to solve nonlinear differential equations.It has been attempted to show the capabilities and wide-range applications of the proposed methods in comparison with a type of numerical analysis as fourth-order Runge–Kutta numerical method in solving this problem.Also,velocity fields have been computed and shown graphically for various values of physical parameters.The objective of the present work is to investigate the effect of Reynolds number and suction or injection characteristic parameter on the velocity field.